Final answer:
The intersection of a cube and a plane passing through four vertices that do not belong to the same face forms a regular tetrahedron, which is a two-dimensional face of a three-dimensional object; therefore, the correct answer is (D) None of the above.
Step-by-step explanation:
The question asks about the intersection of a cube and a plane in three-dimensional space, where the plane passes through four vertices of the cube that do not belong to the same face. As the cube has equal edge lengths of 1, and the vertices through which the plane passes are not on the same face, the intersection of the cube and the plane forms a geometric figure.
The intersection between the cube and the plane is a diagonal plane that cuts the cube into two congruent polyhedra, each with six faces. This figure is known as a regular tetrahedron. Therefore, the correct answer is (D) None of the above, since the intersection is a two-dimensional face of a three-dimensional object, which is not a line, a point, nor a complete plane as described in options (A), (B), and (C) respectively.